(122e) Dynamic Mechanisms of a Vibration Bed under Weakly Excitation

Many studies have shown that a granular bed can be fluidized and several different kinds of complicated phenomena under external vibrations can be generated, such as heaping, pattern formation, convection, fluidization, size segregation, surface wave, and arching. However, most previous works focused on the vibrated system under strong vibration, and very few studies investigated the dynamic mechanisms of particles under a weakly excited system. The paper intends to investigate the dynamic mechanisms of particulates of a weakly vibration bed.

Figure 1 shows the schematic drawing of the experimental apparatus. A Techron VTS-100 electromagnetic vibration system was employed as the vertical shaker. The shaker was vertically driven by sinusoidal signals produced by a function generator (Meter Inc. DDS FG-503) through a power amplifier (CE1000 Power Amplifier). The vibration frequency f and the vibration acceleration a were measured by a Dytran 3136A accelerometer fixed at the shaker and connected to an oscilloscope (Tektronix TDS 210). The vibration radian frequency w and the vibration amplitude r could be calculated from w = 2pf and r = a/w², respectively. The dimensionless vibration acceleration G and the dimensionless vibration velocity V_b were defined as G = a/g and V_b = rw/(gd)^1/2, respectively, where g is the gravitational acceleration and d is the bead diameter.

The current experiments used glass beads with mean diameter of 1.0 mm (standard deviation: 1.33%) and bead density r_p of 2538 kg/m³ as granular materials. A tank with plexiglass walls was driven by the shaker. The height, width, and depth of the inside space of the tank were 12 cm, 8 cm, and 1.4 cm, respectively.

Granular materials seemed to be solids without external excitations and it could be fluidized by external energy input. The fluidized phenomena start near the surface. The upper region of a vibrating granular bed is more fluidized and excited than the lower region of a vibrating granular bed. The depth of fluidized region increases as the vibration strength increases. Figure 2 shows the schematic drawing of the solid-like region and liquid-like region.

Figure 3 shows the initial setup of a container. It shows that the lower region within 50 mm high was placed with white glass beads with mean diameter of 1.0 mm and one more layer of 10 mm high was placed with red glass beads with the same size. The layer of red beads was served as the tracer particles of the whole bed, and it could move downward as a container was driven by external vibration. Therefore, the mixing region of white and red beads was measured as a liquid-like region and non-mixing region was defined as a solid-like region. The experiments were performed in a shaker for different accelerations with various different frequencies.

The height of solid-like region decreases with increasing vibration strength. The granular materials were like bulk solids of the smaller vibration conditions and the state was defined as a completely solid-like region (CSLR). As the vibration strength increases above a critical value (G_s), the liquid-like region (LLR) occurs. With continually increasing the vibration strength up to another critical value (G_l), the state of fully liquid-like region (FLLR) achieves. The above dynamic states for different vibration conditions were shown in figure 4. The effects of vibration conditions on height of solid-like region and depth of liquid-like region were discussed in the paper.

Figure 1: The schematic drawing of the experimental setup

Figure 2: The schematic drawing of the liquid-like region and solid-like region

Figure 3: The initial setup of a container

Figure 4: The phase diagram for different vibration conditions